Meds interactions questions

Hello,
I have Hashimoto and take both Eltroxin for the Hypo and Seroquel and Haloperidol for psychosis which might be connected to the Hashimoto, my question is could the antipsychotics cause the TSH to rise and fluctuate, currently I am on 900 mcg/week and my TSH at the past few months went from ~7 to ~3 to ~0.5 to ~2.5 and now 6.5?
If yes, shall the increase in the TSH be addressed by increasing the Eltroxin dose or it will settle by it self? and if one day my Psychiatrist stop my Antipsychotics, will this cause the dose of Eltroxin to be reduced?

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